报告题目：Local distortion, multiplicity and boundary behavior of harmonic mappings

报 告 人：Antti Rasila副教授（广东以色列理工学院）

报告时间：2022年6月20日  14:30-15:30

报告地点：理学院五楼数学研究中心智慧教室

报告摘要：

We discuss generalizations of classical boundary behavior results, called the Caratheodory boundary extension theorem and the Koebe lemma, to harmonic and related classes of mappings. The first of these results states that a univalent analytic function between two Jordan domains does have a homeomorphic boundary extension. The second one shows that if an analytic function tends to a point along arcs approaching a boundary arc of the unit disk, then the function is must be a constant.

Univalent harmonic mappings, in general, do not have these properties. Indeed, by using the Poisson integral formula, it is possible to construct a simple example of a harmonic mapping that has both "expanding" boundary points where the cluster set corresponds to a line segment, thus breaking the boundary continuity, and boundary arcs collapsing to points, which breaks the Koebe property. Notably, both of the aforementioned results hold for quasiconformal mappings. 

In this talk we discuss generalizations of these results for non-quasiconformal harmonic mappings under assumptions involving the local distortion and multiplicity (valency) of the mapping.

报告人简介：

Antti Rasila，广东以色列理工学院副教授。主要研究方向为复分析，特别是拟共形映射和调和映射，在《Adv. Math.》《Calc. Var. Partial Differential Equations》《Math. Z.》《SIAM J. Sci. Comput.》等国内外数学杂志发表学术论文60余篇。